Circular motion worksheet with answers

Free printable Circular motion worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.8 m/s². What is the smallest radius r_min for a curve taken at 160 km/h?

v = 160 km/ha_max = 0.8 m/s²

r_min = m

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.5 m/s². What is the smallest radius r_min for a curve taken at 160 km/h?

v = 160 km/ha_max = 1.5 m/s²

r_min = m

3.Medium

A curve of radius 230 m is banked at 5°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 230 mθ = 5°g = 9.81 m/s²

v = m/s

4.Medium

A car drives over the top of a hump in the road, which is a circular arc of radius 100 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

r = 100 mg = 9.81 m/s²

v_max = m/s

5.Hard

A 1.8 kg ball on a string 0.8 m long is swung in a vertical circle. At the lowest point it moves at 4 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.8 kgr = 0.8 mv = 4 m/sg = 9.81 m/s²

T = N

6.Hard

A 1.5 kg cart is released from rest at a height of 19.8 m on a frictionless track and runs through a vertical loop of radius 5.5 m. Use g = 9.81 m/s². Find the normal force N_bottom of the track on the cart at the bottom of the loop.

m = 1.5 kgh = 19.8 mR = 5.5 mg = 9.81 m/s²

N_bottom = N

Answer key

1. r_min = 2469 m
2. r_min = 1317 m
3. v = 14.05 m/s
4. v_max = 31.32 m/s
5. T = 53.66 N
6. N_bottom = 120.7 N

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